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STEEL STRUCTURES FOR TALL BUILDINGS

1

TALL BUILDINGS

Depending on the place where the building is located and also on its height, the

action of the wind can be more or less severe than the seismic action. As a result,

one of the three requirements:

resistance;

rigidity;

ductility;

becomes more important to satisfy.

In situations where the action of the wind is more severe, the rigidity requirement is

more important, because the response of the structure must remain in the elastic

range. On the other hand, in situations where the seismic action is more severe, the

ductility requirement is more important, to be able to dissipate the energy.

Specific requirements are:

structural requirements;

technological and functional requirements.

1.1.1. Steel structural systems

The structure of a building usually consists of a set of plane frames, to ensure

spatial behaviour. Basically, there are three types of plane frames (Fig. 1.1). In all

these three cases, the beam-column connection must be rigid.

MRF EBF CBF


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MRF CBF EBF

MRF moment resisting frame

CBF concentrically braced frame

EBF eccentrically braced frame

Fig. 1.1.Types of plane frames

The eccentrically braced frames (EBF) were created by Egor Paul Popov

(1977) at the University of California, Berkeley (died April 19, 2001). A comparison of

the main features of these three systems is presented in table 1.1.

Table 1.1.Characteristics of structural systems plans

MRF CBF EBF

Resistance good good good

Rigidity low very good good

Ductility very good low good

Commentaries on the loading state and on the energy dissipation.

The most recent structural solutions try to better control the response of the

structure. They can be classified as:

passive

o base isolation

o dampers

o tuned mass dampers

o buckling-restrained braced frameso the use of low yield steel


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active

Commentaries separation of functions:

resistance moment frames;

rigidity braces; ductility dampers.

Depending on the height of the building and mainly on the ratio between the

height Hand the dimension in plan B, the most commonly used structural solutions

for resisting horizontal forces are the following ones:

moment frames (Fig. 1.2a);

frames with vertical bracings (Fig. 1.2b);

frames with vertical bracings and outriggers (Fig. 1.2c); structures with beam-walls (Fig. 1.2d);

tubular structures (Fig. 1.2e);

multi-tube and mega-frame structures (Fig. 1.2f);

tube in tube

bundled tubes.

(a) (b) (c) (d) (e) (f)

Fig. 1.2.Types of structural systems

2B

H

4B

H

4B

H

6B

H

6B

H

8

B

H


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The location of seismic systems in a building depends on structural,

architectural, technological and functional requirements. Generally, codes (EN 1998-

1, P100-1:2013) classify seismic structural systems in:

moment frames (Fig. 6.1 EN 1998-1);

Fig. 1.3.Moment resisting frames

frames with concentric bracings (Fig. 6.2 EN 1998-1) (Fig. 6.3 EN 1998-1);

Fig. 1.4.Frames with concentric bracings

frames with eccentric bracings (Fig. 6.4 EN 1998-1);


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Fig. 1.5.Frames with eccentric bracings

inverted pendulum structures (Fig. 6.5 EN 1998-1);

Fig. 1.6.Inverted pendulum structures

structures with concrete cores and concrete walls (Fig. 6.6 EN 1998-1);

Fig. 1.7.Structures with concrete cores and concrete walls

moment frames combined with concentric braces (Fig. 6.7 EN 1998-1);


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Fig. 1.8.Moment resisting frame combined with concentric bracing

moment frames combined with infills (Fig. 6.8 EN 1998-1);

Fig. 1.9.Moment resisting frame combined with infills

1.2. SEISMIC DESIGN PRINCIPLES OF METAL STRUCTURES

1.2.1. The capacity design concept

The modern seismic design approach is based on the idea that much of the

energy induced by the earthquake in the structure is dissipated by means of plastic

mechanisms; generally, it is not efficient to resist this action only in the elastic range,

unless under very special circumstances, such as the case of nuclear power plants

etc. Current trends are to better control energy dissipation, meaning the behaviour of

the structure in the post-elastic range. The basic idea is to use a plastic mechanism

which is chosen, directed and controlled by the engineer, and to ensure conditions

so that all other elements remain essentially in the elastic range until the moment

when the mechanism has exhausted its capacity of dissipation. Subsequently to thisprinciple, plastic deformations are accepted only in selected areas generally located


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in beams in a neighbouring area to the joint and, in the end, at the base of the

columns or at their top end.

The designer choses the potentially plastic zones on the structure (their type

and location) and the rest of the structure must remain basically in the elastic range

while the chosen plastic zones keep on plastifying. This means that the rest of the

structure must be able to resist, basically in the elastic range, the loads (efforts)

generated by the action that fully plastifyies all the chosen potentially plastic zones.

Following this, all the parts of the structure that are outside of the potentially plastic

zones must resist efforts associated to the capacity of the chosen plastic

mechanism, considering not the minimum values of the plastic resistance of these

zones but probable (expected) ones. This is basically the meaning of the capacity

design concept.

Remark: A higher resistance of the potentially plastic zones can either put in danger

the non-dissipative zones of the structures (as failures may occur there) or lead to

oversize of the entire structure.

1.2.2. Basic concepts

Ductility

Generally, ductility is the ability of energy dissipation in the plastic range. It is

expressed as ratio between ultimate displacement and the value of the same

displacement corresponding to the yielding limit.

Plastic hinge

It is a concept that defines a cross-sectionof the structural member in which

the ability to resist an increasing bending moment has been exhausted. Plastic

hinges do not exist in reality; plastic deformations develop over a certain length of

the element, so they are not located in one section, as the model presumes.

Class of the cross-section

Depending on the occurrence of local buckling of the components of a cross-

section that is subjected to bending moment, four classes of cross-sections are

defined in EN 1993-1-1. Depending on the class of the cross-section, the loading

state of the structural member can be determined using elastic or plastic analysis


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and the resistance of the cross-section can be expressed in the plastic, elastic or

critical range (Fig. 1.10).

Fig. 1.10.Evolution of the stress state in a cross-section subject to bending moment

1.2.3. The main steps of seismic design of the structure

The capacity design concept tries to better manage the behaviour of the

structure in the elastic and in the plastic range till failure. The following steps are

recommended to be followed to achieve a good behaviour of the structure:

1. Chosethe structural systemand the model of the structure.

2. Estimate the loadsin each loading case.

3. Estimate the masses. The masses are calculated corresponding to the loading

situation that contains the seismic action. They are therefore associated to the

gravitational loads that are defined by long-term factors applied to the nominal

values of the loads.

4. Pre-size structure by choosing the position of the plastic zones, implicitly the

plastic mechanism of energy dissipation. Cross-sections are proposed for all

structural members.

5. Performinga modal analysis of thestructure, for determining the eigenperiods

and the distribution of equivalent static forces corresponding to each eigenmode.

6. Performing a static analysis of the structure. In this step, a number of

eigenmodes are taken into account to estimate the resulting seismic forces.

max< fy max= fy max= fy max= fy

y y

z

z

class 4

class 3

class 2

class 1


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7. Chosethe cross-sections of themembers in plastic zonesto resist the efforts

generated by the action of the seismic base shear (Fb).

8. Estimate the plastic reserve () of the chosen plastic mechanism.

9. This reserve is taken into account by amplifying the seismic force by the

factor(while the gravitational loads remain unchanged). Do another static analysis

for this amplified seismic force (Fb). The rest of the structure (except the

selected plastic areas) must remain essentially in the elastic range while the

chosen plastic mechanism dissipates energy, so all theother memberswill be

sized to resist the efforts generated by this amplified seismic force. This

amplified seismic force (Fb) can also be determined using a virtual work

equation:Lext= Lint (1.1)

where:

Lextis produced by seismic force;

Lintis produced by efforts in the dissipative elements.

In the absence of a more rigorous analysis, some codes recommend penalising

values. For instance, the American code ANSI/AISC 341-10 and the Romanian

code P100-1:2013 recommend the following values for the global overstrength

factor of the structure(Tab. 1.2).

Table 1.2.Values for the global overstrength factor of the structure([3] Tab. F.1)

Structural system

a) Moment frames 3,0

b) Concentrically braced frames 2,0

c) Eccentrically braced frames 2,5d) Inverted pendulum structures 2,0

e) Dual frames

- moment frames + concentrically braced frames

- moment frames + eccentrically braced frames

2,0

2,5

f) Frames with buckling-restrained braces 3,0


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These recommendations apply in the situation where the structure complies with

the rules of conformations given in the codes ANSI/AISC 341-10 or P100-1:2013

for a good post-elastic behaviour of the structure.

10. Chosethe cross-sections of themembers outside the plastic zonesto resist

the efforts generated by the action of the amplified seismic force (Fb).

11. Return to step 5 and perform a new static analysisfor the new cross-sections

of the structural members, taking into account the seismic base shear (Fb)and,

respectively, the amplified seismic force (Fb) and follow steps 5-10 to tune up

the structure.

12. Perform a push-over analysis(post-elastic analysis)to verify that the chosen

plastic mechanism is developed and the required ductility can be obtained.13. Improve the structure based on the results of the push-over analysis (by

changing the cross-sections of some members) and follow steps 5-12 to tune up

the structure for as many times as it is necessary.

14. Perform a time-history analysis (dynamic analysis) using accelerograms,

which can be either real or fabricated. It can be done in the elastic or in the

plastic range.

15. Improve the structure based on the results of the time-history analysis (by

changing the cross-sections of some members) and follow steps 5-14 to tune up

the structure for as many times as it is necessary.

1.3. ESSENTIAL SEISMIC REQUIREMENTS FOR THE METAL STRUCTURES

FOR TALL BUILDINGS

1.3.1. Classifications

Present day codes distinguish between the types of structures, depending on

their plastic behaviour. Basically, there are two types of structural concepts:

low dissipative structural behaviour;

dissipative structural behaviour.

These two types of behaviour are well distinguished in the European standard EN

1998-1 [10], in the Romanian code P100-1:2013 [11] and in the American code


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ANSI/AISC 341-10 [12]. Subsequently, three types of structures, depending on their

post-elastic behaviour, can be distinguished in the three standards [10], [11]:

DCL (limited ductility class) [10], [11] capable to undergo minimum plastic

deformations under the effects of the seismic action; EN 1998-1 [10] acceptsthem in the case of buildings without isolation of the base, only in regions with

low seismicity; in ANSI/AISC 341-10, they are calledordinary structures(OMF,

OCBF, OEBF etc.);

DCM (medium ductility class) [10], [11] capable to undergo limited plastic

deformations under the effects of the seismic action; in ANSI/AISC 341-10, they

are calledintermediate structures(IMF, ICBF, IEBF etc.);

DCH

(high ductility class) [10], [11] capable to undergo significant plasticdeformations under the effects of the seismic action; in ANSI/AISC 341-10, they

are calledspecial structures(SMF, SCBF, SEBF etc.).

Table 1.3. Design concepts, structural ductility classes and upper limit reference

values of the behaviour factors([3] Tab. 6.1)

Design concept Structural ductility

class

Range of the reference

values of the behaviourfactor q

Concept a)

Low dissipative structuralbehaviour

DCL (Low) 1,5 - 2

Concept b)

Dissipative structural behaviour DCM (Medium)4

also limited by thevalues of Table 1.4

DCH (High) only limited by thevalues of Table 1.4

Table 1.4.Upper limit of reference values of behaviour factors for systems regular in

elevation([3] Tab. 6.2)

Structural type Ductility Class

DCM DCHa) Moment resisting frames 4,0 5u/1


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b) Frame with concentric bracings

- Diagonal bracings

- V-bracings

4,0

2,0

4,0

2,5

c) Frame with eccentric bracings 4,0 5u/1

d) Inverted pendulum 2,0 2u/1

e) Structures with concrete cores or concrete walls See R.C. section

f) Moment resisting frame with concentric bracing 4,0 4u/1

g) Moment resisting frames with infills

- Unconnected concrete or masonry infills, in contactwith the frame

2,0 2,0

- Connected reinforced concrete infills See composite section

- Infills isolated from moment frame (see momentframes)

4,0 5u/1

1.3.2. Some structural requirements for seismic resistant steel structures

1. The structure will follow the principle strong column weak beam to avoid

the appearance of floor mechanisms.

2. Kbracings where the intersection of the diagonals is located on the column are

not accepted in seismic resistant structures (Fig. 1.11) because of the

unbalanced horizontal force that acts on the column after buckling of the

compressed diagonal. In the case of V (or inverted V) bracings, the beam

containing the intersection point of the diagonals must be continuous in that point

and sized to resist gravitational loads neglecting the presence of the braces.

Fig. 1.11.Recommendations for the bracing system

3. All structural members and their connections must remain essentially in the

elastic range under the action of the seismic base shear force (Fb).


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4. For earthquakes that can generate forces superior to the seismic base shear

(Fb), the structure must be able to dissipate energy using a plastic mechanism.

The mechanism must be chosen, managed and controlled by the designer and

plastic deformations must develop only in chosen zones. The beginning of plastic

behaviour of the structure must be done under the action of the force Fb.

5. The state of efforts and deformations induced on the structure by the maximum

ground acceleration (peak ground acceleration on the location) must be

estimated. A non-linear dynamic analysis is recommended for this purpose. In

this state the structure shall comply with the following requirements:

all structural members and their connections must be essentially in the

elastic range except the chosen plastic zones;

all lateral displacements (Fig. 1.12) must meet the "drift" requirements

given in codes;

Fig. 1.12.Limitation of lateral displacement ("drift")

all plastic deformations in the plastic zones must not exceed the ultimate

plastic deformation allowed for these zones (material and cross-section

limitations).6. No other ultimate limit state (general instability, brittle fracture etc.) should be

reached before the formation of the plastic mechanism.

7. The acceptable plastic deformations are as follows:

plastic hingesin the members in bending:

at the ends of the beams, preferably not in the beam-column

connection (Fig. 1.13a), even though EN 1998-1 accepts it;

different research programs try to investigate the plastic behaviourof these connections;

v

h


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at the ends of long linksin eccentrically braced frames (EBF);

at the ends of intermediate links in eccentrically braced frames

(EBF); in this case the influence of the shear force on the plastic

moment resistance cannot be neglected. at the base of the frameor at the top of the columns(Fig. 1.13b,

c) in the upper storey of multi-storey buildings after the formation of

at least 50% of the plastic hinges in the beams;

at the top and bottom of columns in single storey buildings in

which NEd in columns conform to the inequality: NEd/Npl,Rd < 0,3

(Fig. 1.13b, c); the same approach can be used for inverted

pendulum structures, provided that the earthquake resistantstructure possess more than one column in each plane;

(a) (b) (c)

Fig. 1.13.Recommended locations for plastic hinges

yielding of the tension diagonal in frames with concentric bracings;

shear yielding in the webs of short beams and short links.

8. The following are forbidden in potentially plastic zones:

change the cross-section of the element;

to have holes;

to support other secondary (or main) structural members.

9. Plastic deformations are not allowed in the following locations:

all along the columns (except for the locations at point 7);

in the joints (panel zones) of the structure (see the notes below);

in the anchor bolts of the columns;

in the connections of members (see the notes below).

Note 1: More recent codes do not explicitly forbid plastic deformations in the

panel zone. EN 1998-1 and P100-1:2013 do not say anything about the panel

rather not

recommended

recommended

recommended


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zones. ANSI/AISC 341-10 has specific provisions concerning the (column) panel

zone (Fig. 1.14).

Note 2: ANSI/AISC 341-10 limits the slenderness of the panel zone. Many

tests demonstrated that significant ductility can be obtained by shear yielding of

the panel zone (ANSI/AISC 341-10, page 9.1-201) but excessive panel zone

distortions can unfavourably affect the beam-to column connection. The

Japanese code also accepts yielding in the panel zone, based on the results of

tests.

Note 3: EN 1998-1 accepts to dissipate energy in semi-rigid connections

(connections where a moment-rotation relation is given) if their behaviour is very

well controlled.

Fig. 1.14.The column panel zone in the joint of a structure

10. The cross-sections of the potentially plastic zones (class 1 cross-sections) must

allow the development of plastic deformations without local buckling or other

forms of instability. Plastic deformations shall be directed to the chose potentially

plastic zones.

Generally, codes make a connection between the chosen behaviour (ductility)

factor q and the slenderness of the cross-sections of structural members. For

instance, EN 1998-1 and P100-1:2013 require the following:

Table 1.5.Requirements on cross-sectional class of dissipative elements depending

on Ductility Class and reference behaviour factor([3] Tab. 6.3)

Ductility class Reference value of

behaviour factor q

Required cross-

sectional class


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DCM

1,5 < q 2 class 1, 2 or 3

2 < q4 class 1 or 2

DCH q > 4 class 1

11. The joints and the connections of seismic-resistant structures should remain

essentially in the elastic range for a good plastic behaviour of the entire structure

(see notes at point 9). Local buckling of the joint is not acceptable.

12. Floor mechanisms or other partial (local) mechanisms are not accepted in multi-

storey buildings subjected to seismic actions.

13. The steel grades that are used must fulfil special requirements in order to provide

a good plastic behaviour of the entire structure.

1.3.3. Requirements for steel grades used for seismic-resistant structures

Because of the required good plastic properties, codes provide special

requirements for steel grades used for seismic-resistant structures. P100-1:2013, as

well as previous versions of EN 1998-1 and ANSI/AISC 341-10, contain precise

values for the most important mechanical characteristics of steel. Newer versions of

EN 1998-1 and ANSI/AISC 341-10 tend to be more relaxed, as they make reference

to other design codes. The most important requirements are the following ones:

1. Generally, codes limit the superior value of the yielding limit of steel. As a result,

the commonly used steel grades for seismic-resistant structures are: S235, S275

and S355. One of the reasons for limiting the yielding limit of steel was that one

of the causes of many brittle fractures during the Northridge earthquake (1994)

was that the bigger yielding limit resulted in increased requirements for

connection.

2. The steel grade and the welding material must have an adequate tenacity to

avoid brittle fracture. P100-1:2013 requires 27J on a Charpy specimen at the

minimum design temperature. EN 1998-1 no longer contain explicit values and it

makes reference to other codes. ANSI/AISC 341-10 is more precise in defining

the zones where special requirements apply.


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3. In potentially plastic zones, the actual maximum yielding strength, fymaxshall not

exceed a value that must be written on plans. This limitation is expressed as

follows:

yovmaxy f1,1f (EN 1998-1) (1.2)

yovmaxy ff (P100-1:2013) (1.3)

yyye FRF (ANSI/AISC 341-10) (1.4)

utye FRF (ANSI/AISC 341-10) (1.5)

where:

fy nominal value of the yielding limit (ex. 235N/mm2for S235);

ov overstrength factor;

the recommended value in EN 1998-1 is 1,25;

P100-1:2013 recommends different values: 1,40 for S235; 1,30 for

S275 and 1,25 for S355. However, these values must be correlated

with the locally adopted valueM0=1,1;

RyFy expected yield stress;

RtFu expected tensile strength.

The values of Ryand Rtin ANSI/AISC 341-10 [4] are given in table 1.6.

Table 1.6.Ryand Rtfor steel and steel reinforcement materials([4] Tab. A3.1)

Application Ry Rt

Hot-rolled structural shapes and bars:

- ASTM A36/A36M

- ASTM A1043/1043M Gr. 36 (250)

- ASTM A572/572M Gr. 50 (345) or 55 (380),

ASTM A913/A913M Gr. 50 (345), 60 (415), or 65 (450),

ASTM A588/A588M, ASTM A992/A992M

- ASTM A1043/A1043M Gr. 50 (345)

- ASTM A529 Gr. 50 (345)

- ASTM A529 Gr. 55 (380)

1,5

1,3

1,1

1,2

1,2

1,1

1,2

1,1

1,1

1,1

1,2

1,2

Hollow structural sections:

- ASTM A500/A500M (Gr. B or C), ASTM A501 1,4 1,3

Pipe:

- ASTM A53/A53M 1,6 1,2


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Plates, Strips and Sheets:

- ASTM A36/A36M

- ASTM A1043/1043M Gr. 36 (250)

- A1011/A1011M HSLAS Gr. 55 (380)

- ASTM A572/A572M Gr. 42 (290)

- ASTM A572/A572M Gr. 50 (345), Gr. 55 (380),

ASTM A588/A588M

- ASTM A1043/1043M Gr. 50 (345)

1,3

1,3

1,1

1,3

1,1

1,2

1,2

1,1

1,1

1,0

1,2

1,1

Steel Reinforcement:

- ASTM A615, ASTM A706 1,25 1,25

4. P100-1:2013 requires:

20,1ff yu ;

%20u ;

the elongation at the end of the yielding plateau must be superior to 1,5%;

EN 1998-1 and ANSI/AISC 341-10 no longer contain such explicit limits.

5. Steel must have a good weldability.

6. Bolts to be used are 8.8 and 10.9. 12.9 bolts generally have a brittle failure. For

in-plane loaded connections, the shear resistance must be superior to thebearing resistance in order to have a ductile failure. For end-plate connections,

failure mode 1 (complete yielding of the flange) is the most ductile one.

1.3.4. Requirements for the connections of seismic resistant steel structures

Generally, codes require as basic principle the idea that joints must be able to

transfer the resistances of the elements, taking into account the possibility that the

resistance of the element is greater than its nominal value. To meet this

requirement, codes contain recommendations about conformation, calculation and

technological requirements for joints. Below are presented some of the most

important requirements:

1. The conformation of the joint detail must limit the zones where notch effects

could arise, important residual stresses could develop or where plastic

deformations could occur in the joints (Fig. 1.15).


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Fig. 1.15.Example of joint that avoids notch effects

2. In a connection with weld seams and bolts, loads shall not be shared between

these two different connecting means.

3. It is generally considered that full penetration butt welds are able to transfer the

required resistance.

4. EN 1998-1 [10] and P100-1:2013 [10] require for the resistance of joints realised

with fillet welds and bolts that:

fyovd R1,1R ((6.1) EN 1998-1; (6.1) P100-1:2013) (1.6)

where:

Rfy the plastic resistance of the connected member, calculated based on the

nominal value of the yielding limit;

ov overstrength factor;

Rd resistance required to the joint.

5. Given that welding requires more advanced technology and more skilled workers

(the quality of welding depends primarily on these requirements), the American

and European practice is to realize the shop connections by welding and the site

connections by bolts, thus avoiding welding on site. On the contrary, in Japan,

most of the joints on the site are made by welding.

6. Given that the weld introduces residual stresses and it can be a weak point in the

structure, in the joints of a structure it is generally recommended for the column

to be continuous (Fig. 1.16a). Yet there situations where, for technical reasons, it

is accepted that the beam is continuous (Fig. 1.16b). This type of detail is not

accepted in Romania.

No Yes

1:5

1:5


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(a) (b)

Fig. 1.16.Types of beamcolumn joints

7. It is recommended for the shear resistance of bolts to be superior to the bearing

resistance, in order to have a ductile failure of the connection. To fulfil this

requirement, EN 1998-1 [10] and P100-1:2013 [10] require for the shear

resistance to be 1,2 times superior to the bearing one.

1.4. THE BEAMS OF SEISMIC RESISTANT STEEL STRUCTURES

1.4.1. Conformation principles

The majority of codes recommend realising the beams with three zones (Fig.

1.17):

a rigid zone (r) at each end of the beam, near the beam to column joint;

a plastic zone (p), neighbour to the rigid one;

a central elastic zone (e).


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Fig. 1.17.Zones on a beam sized by the seismic action

Considering the notations (Fig. 1.17):

r

EdM the maximum bending moment in the rigid zone (r

E,Ed

r

G,Ed

r

Ed MMM += );

rp

EdM the bending moment in the cross-section between the rigid zone and the

plastic one ( rp E,Edrp G,EdrpEd MMM += );

pe

EdM the bending moment in the cross-section between the plastic zone and the

elastic one ( pe E,Edpe

G,Ed

pe

Ed MMM += );

during an earthquake, the gravitational loads remain unchanged, while the effects of

the seismic action can increase.

Following this, we consider a monotonic increase of the bending moments

caused by the seismic action. Failure of the beam-column connection (cross-section

r) must be avoided ( rRdr

Ed MM < ). Consequently, the first cross-section fully plastic is

(rp) (on the right hand side in figure 1.17) ( plrprp MM = ). If the bending moment caused

by the seismic action increases, the plastic deformations develop towards cross-

section (pe). In the state when the bending moment in cross-section (pe) is equal to

the plastic resistance of the cross-section ( plpepe MM = ) we have plastic stress

distribution on the entire cross-section all along zone (p), where we accepted the

development of a plastic hinge. In this loading state, cross-section (r) must still

ME

r rep p

MG


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remain basically in the elastic range ( rRdr

Ed MM < ). If the bending moment caused by

the seismic action continues to increase, rotations occur in the already formed

plastic hinge and, at a certain moment, a second plastic hinge will begin to form.

This second plastic hinge must not be located in zone (r) (on the left hand side in

figure 1.17) but in zone (p). Following a similar scenario, the entire cross-section

goes plastic all along zone (p) (on the left hand side in figure 1.17). If the beam is

properly sized, at this stage, zones (r) must be still basically in the elastic range and

zone (e) must be in the elastic range.

To get this behaviour, the cross-section in the plastic zone (p) must be class

1, the cross-section in the rigid zone (r) may be class 1 or 2 (preferably class 1) and

the cross-section in the elastic zone (e) may be class 1, 2 or 3 (preferably class 1 or

2). The length of the rigid zone (r) (Fig. 1.17) is also very important. Basically, it must

not be too long, to reduce the increase of the bending moment between the plastic

hinge and the beam to column connection. If the plastic hinge is too much away

from the column face, in order to avoid the weak column, the requirements for the

column cross-section increase. On the other hand, the rigid zone must be sufficiently

long to allow a good stress distribution in the flange between the plastic hinge cross-

section and the beam to column connection.Basically, plastic deformations in the structure must begin to develop under

the action of thebase shear force (Fb) (when the equivalent seismic force reaches

this value), so, the first plastic hinge must form in a structure in a beam once that the

value of the seismic force overcomes thebase shear force (Fb).

1.4.2. Types of practical solutions for beams

There are basically two types of practical solutions to direct the formation of

the plastic hinge in the beam at a certain distance from the beam to column

connection:

strengthening the rigid zone (Fig. 1.18) relative to the rest of the beam; the

solution in figure 1.18a shows an additional risk of lamellar tearing of the material

in the flange of the column, because of the welding seams;


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23

(a) (b)

Fig. 1.18.Examples of solutions for strengthening the rigid zone (FEMA 351 [4] Fig.

2.3, FEMA 350 [4] Fig. 3.23)

reducing the beam cross-section (Fig. 1.19) in zone (p); this solution is also

known as RBS (reduced beam section) or dog bone.

RBS solution was patented in the United States by the manufacturer ARBED of

Luxembourg in 1992. After the Northridge earthquake (1994) they gave up their

intellectual property rights, which facilitated the evolution of this solution. The detail

in figure 1.19a reduces the stress concentrations. Tests showed that plastic

deformations develop all along the plastic zone. The detail in figure 1.19c tries to

follow the bending moment diagram and to generate a uniform yielding state along

the plastic zone. Tests showed that, after some plastic deformations, brittle fractures

may occur in the reduced sections in figures 1.19b and 1.19c because of the corner

areas, which are load concentrators.

Fig. 1.19.Examples of solutions for the reduced beam section

(a)

(b)

(c)


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24

1.4.3. Example of RBS design

Generally, there are two types of requirements of major importance in the

choice of the cross-sections of beams (and other structural members). They do not

refer to the reduced beam section zone (RBS) but to the beam cross-section:

the cross-section of the beam must be able to resist the bending moment

generated by the load combination containing amplified seismic forces;

r

E,EdT

r

G,Ed

r

Ed MMM += ((6.6) P100-1:2013) (1.7)

r

E,Edov

r

G,Ed

r

Ed M1,1MM += ((6.6) EN 1998-1) (1.8)

where:

r

EdM the total bending moment in the beam to column connection;

r

G,EdM the bending moment generated by gravitational loads;

r

E,EdM the bending moment generated by seismic loads;

T the value of the overstrength of the structural system (see Tab. 1.2);

the minimum value of the plastic reserve of all plastic hinge cross-sections;ov the overstrength factor (of the material in the plastic hinge zones);

the structure must fulfil the drift requirement (Fig. 1.12);

limh

v (1.9)

the displacement v in relation (1.9) is calculated without reducing the forces by

the behaviour factor q.

Generally, the drift requirement (1.9) is more difficult to be fulfilled for moment

frames. The reduction of the cross-section in the plastic hinge zone reduces the

rigidity of the frame. Researches carried out by Grubbs at the University of Texas

[16] showed that a 50% reduction of the flanges in the RBS zone reduces the rigidity

of the frame by 6 7%, while a 40% reduction of the flanges in the RBS zone

reduces it by 4 5%.

In a first iteration, the cross-sections of members (beams, columns, braces

etc.) are chosen, based on the drift requirements. Class 1 and 2 cross-sections can

be sized either in the elastic or in the plastic range.


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25

The main steps of design are the following ones:

1.4.3.1. Estimation of the position of the plastic hinge

If the loads generated by gravitational loads are less than 30% of the

resistance of the cross-section of the beam, the American code FEMA 350 [17]

recommends the following relations.

Fig. 1.20.Moment frame with plastic hinges on the beams (FEMA 350 [4] Fig. 3.23)

If gravitational loads generate more than 30% of the loads in the beam cross-

section, a plastic analysis of the structure is necessary to determine the position of

the plastic hinges. FEMA 350 [17] recommends values for the distance sh(Fig. 1.21)

for different types of details of beam to column connection. Generally, this value is

around:

2

h

2

hs bch += (1.10)

where:

hc the height of the cross-section of the column ;

hb the height of the cross-section of the beam.

deformed frame

plastichinges

initialform

h

L

L1


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26

Fig. 1.21.Location of the plastic hinges

Depending on the type of detail, the distance shmay increase up to:

bc

h h2

hs += (1.11)

Generally, the length of the plastic hinge in steel structures beams is about half of

the beam height (hb/2) [17]. FEMA 350 [17] recommends the following values for the

dimensions in figure 1.22:

Fig. 1.22.Geometry of RBS (reduced beam section)

( ) fb75,0...50,0a = (1.12)

( ) bh85,0...65,0b = (1.13)

1.4.3.2. Estimation of the probable value of the bending moment in the plastic hinge

plastic hinge

L1

L

sh

hb hc

ab

c

c8

bc4R

22

+=

bf


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27

The aim of this sizing procedure is to limit the maximum bending moment that

may occur in the cross-section of the beam to column connection at a value inferior

to 85100% of the plastic moment resistance of the cross-section (Fig. 1.23). The

following steps need to be followed to fulfil this requirement:

1. the value of cis proposed (Fig. 1.23);

fb25,0c (1.14)

2. the plastic strength modulus Wpl,RBSof the reduced section (RBS) is determined;

3. the probable valueof the plastic bending moment prRBS,plM of the reduced cross-

section (RBS) is determined (Fig. 1.23); this estimation intends to manage the

possibility for the plastic bending moment in the plastic hinge cross-section to be

bigger than the nominal value;

in the spirit of EN 1998-1 and P100-1 :2013:

RBS,plyovpr

RBS,pl Wf1,1M = (1.15)

where:

fy the nominal value of the yielding limit;

ov overstrength factor; the recommended value in EN 1998-1 is 1,25;

1,1 a safety variation of 10%;

in the American code FEMA 350 [17]:

yeypr

pr

RBS,pl FZRCM = ((3.1) FEMA 350 [17]) (1.16)

where:

Fy the nominal value of the yielding limit;

Ze the plastic strength modulus Wpl,RBS;

Ry factor given in ANSI/AISC 341-10 [4] (see Tab. 1.6);

Cpr factor taking into account strain hardening and other phenomena

that can lead to overstrength; FEMA 350 [17] recommends the relation

y

uy

prF2

FFC

+= ((3.2) FEMA 350 [17]) (1.17)

Fu the nominal value of the ultimate strength;

Cpr= 1,2 may be used in the absence of other information;


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28

Fig. 1.23.Bending moment diagrams

1.4.3.3. Estimation of the shear force in the plastic hinge

The maximum shear force is calculated writing (Fig. 1.24):

2

Lq

L

MMV 1

1

pr

RBS,pl

pr

RBS,pl

RBS

+

+= (1.18)

2

Lq

L

MMV 1

1

pr

RBS,pl

pr

RBS,pl

RBS

+

+= (1.18)

Bending moment resistance of the beam (MRd)

Necessary ending moment resistance

Probable moment

L1

L1

L

sh

q

VRBS VRBS

prRBS,plM

prRBS,plM

pr

RBS,plM

RBS,plM


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29

Fig. 1.24.Equilibrium of the beam segment between the plastic hinges

1.4.3.4. Estimation of the requirements for the critical cross-section

The bending moment in the critical cross-sections rEdM at the face of the

column (Fig. 1.25a) and cEdM in the axis of the column (Fig. 1.25b) is estimated,

based on the following relations:

++=2

baVMM RBS

pr

RBS,pl

r

Ed (1.19)

hRBSpr

RBS,plcEd sVMM += (1.20)

The (plastic) resistance of the beam cross-section is:

0Mypl

r

Rd,pl fWM = (1.21)

The following requirement is checked:

( ) r Rd,plr

Ed M00,1...85,0M = (1.22)

If rEdM is bigger thanr

Rd,plM , cmust be increased (Fig. 1.22) and return to 1.4.3.2.

(a) (b)

Fig. 1.25.Estimation of the requirements for the critical cross-sections

1.4.4. Checks

sh

r

EdM c

EdM

VRBS VRBS

+2

ba

pr

RBS,pl

M prRBS,pl

M


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30

1.4.4.1. Resistance checks

The three zones of the beam (rigid zone, plastic zone, elastic zone) must be

checked with the following relations:

00,1M

M

Rd,pl

Ed ((6.2) EN 1998-1; (6.2) P100-1:2013) (1.23)

15,0N

N

Rd,pl

Ed ((6.3) EN 1998-1; (6.3) P100-1:2013) (1.24)

50,0V

V

Rd,pl

Ed ((6.4) EN 1998-1; (6.4) P100-1:2013) (1.25)

For class 3 cross-sections, the plastic values of the resistance must be replaced by

the elastic ones. The axial force limitation (1.24) is necessary only in the plastic

zone. The values of the resistance in relations (1.23), (1.24) and (1.25) are

calculated as follows:

0MyplRd,pl fWM = for class 1 and 2 cross-sections (1.26a)

0MyelRd,el fWM = for class 3 cross-sections (1.26b)

0MyRd,pl fAN = (1.27)

0M

yv

Rd,pl

3fAV

= (1.28)

where:

A the area of the cross-section of the beam;

Av the shear area of the cross-section of the beam;

M0 partial (safety) factor for resistance of the cross-section; M0= 1,0

(EN 1998-1; EN 1993-1-1) ; M0= 1,1 (P100-1:2013);

Wpl the plastic strength modulus of the cross-section of the beam;

Wel the elastic strength modulus of the cross-section of the beam;

For seismic structures, the use of class 1 and 2 cross-sections is recommended.

The efforts in relations (1.23), (1.24) and (1.25) are as follows:

for the plastic zone (p);

p

E,Ed

p

G,Ed

p

Ed MMM += (1.29)

p

E,Ed

p

G,Ed

p

Ed NNN += (1.30)


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31

p

M,Ed

p

G,Ed

p

Ed VVV += ((6.5) EN 1998-1; (6.5) P100-1:2013) (1.31)

\ p M,EdV the design shear force associated to the application of the plastic

bending moments with opposite signs in both plastic hinge zones;

L

MMV

p

B,Rd,pl

p

A,Rd,plp

M,Ed

+= (1.32)

L the span of the beam; it should be the distance between the two plastic

hinges design shear force associated to the application of the plastic bending

moments with opposite signs in both plastic hinge zones (L1in figure 1.24);

for the rigid zone (r) and for the elastic zone (e);

E,EdTG,EdEd MMM += (1.33)

E,EdTG,EdEd NNN += (1.34)

E,EdTG,EdEd VVV += (1.35)

where:

G,EdE effort (M, N, V) caused by gravitational loads;

E,EdE effort (M, N, V) caused by seismic loads;

M

ovT 1,1 = (1.36)

T the global overstrength factor;

=

i,Ed

i,Rd,plM

M

Mmin (1.37)

1.4.4.2. Lateral torsional buckling check

The lateral stability of the beam shall be checked presuming that a plastic

hinge occurred near the most loaded end of the beam. Both flanges of the beam

must be blocked against lateral displacements in the plastic hinge zone. Codes

generally require for these lateral supports to be able to resist a certain force; for

instance, P100-1:2013 recommends a force equal to 0,06ovfytfbf. Lateral torsional

buckling of the beam must be prevented on the entire length of the beam.

Recommendations for the maximum distance between lateral supports can be foundin EN 1993-1-1.


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32

1.4.5. Constructional recommendations for beams

1. None of the following is not permitted in the plastic zone (p):

to support secondary beams;

to change the cross-section of the beam;

to drill holes.

2. The connection between the beam flange and the column flange (beam web in

the same plane with the column web) shall be realised by fully penetrated but

weld (Fig. 1.26).In figure 1.26, tbfis the thickness of the flange and (FEMA 350 [4]):

1 bevel as required for selected groove weld procedure;

2 max (tbf ;13mm) (+ 0,5tbf ; 0,25tbf );

3 0,75tbf tbf19mm (6mm);

4 minimum radius 10mm (plus not limited, minus 0);

5 3tbf(13mm);

FEMA 353 [XX] covers the requirements for fabrication details, including cutting

methods and smoothness.

Fig. 1.26.Recommended welding detail for beam flange (FEMA 350 [4] Fig. 3.5)

3. The connection between the web of the beam and the column can be realised

either by fillet weld or by butt weld. The bolted connection should be avoided (in


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33

combination with flanges welded connection). If, for technological (erection)

reasons, a bolted connection is used on site, eventually, welding seam must be

realised (Fig. 1.27).

Fig. 1.27.Connection detail (ANSI/AISC 358-10 [4] Fig. 8.1)

4. It is desirable for the beam-column connections to be realised in the shop (by

welding), so that a very good behaviour can be obtained even for very severe

earthquakes. Under these circumstances, it is recommended for the site

connection to be placed in the elastic zone of the beam and, consequently, the

columns arrive on site with the rigid and plastic zones of the beams already

attached. The site connections are made by high strength bolts in slip

connections. The drawback is related to transport, as it is not always easy for

such column parts. However, it is to note that many builders prefer an end-plate

beam-column connection and this cannot be neglected.

5. The beam-column connection must be able to transfer loads corresponding to

the resistance of the connected part (beam), taking into account the overstrength

of the material in the beams.

6. Lateral torsional buckling of the beam must be prevented. Lateral stability of the

top flange is ensured by the reinforced concrete slab by means of the studs that

connect them to avoid relative slip. Special attention must be given to the bottom

flange, as lateral supports must be offered (for instance, by means of a

connection to the slab). It is recommended to avoid any connection between


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34

the slab and the top flange in the plastic zone (and in the rigid zone) [17]

(tests showed that the important increase of the cross-section because of this

connection, as concrete is in compression and steel in tension, can lead to brittle

fracture in the bottom flange when the beam is subject to cyclic loading [17]). An

increased bending moment resistance of the cross-section of the beam also

increases the risk of forming a plastic hinge on the column, instead of having it

on the beam, as desired.

7. It is recommended to have stiffeners at both ends of the plastic hinge (Fig. 1.28).

The thickness of the stiffener, tst, must be at least 75% of the thickness of the

web and bigger than 10mm. It is also recommended to be bigger than bst/15,

where bstis the width of the stiffener. The stiffener width must obey the following

relation:

stwst btb2 =+ (1.38)

where twis the thickness of the web.

Fig. 1.28.Stiffeners on the plastic hinge zone

1.5. THE COLUMNS OF SEISMIC RESISTANT STEEL STRUCTURES

1.5.1. General recommendations

The cross-sections of columns can be one of the following ones:

open cross-sections (Fig. 1.29a);

hollow cross-sections (Fig. 1.29b).

They can be either hot-rolled or built-up by welding.

tw

tr br

bf


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35

(a) (b)Fig. 1.29.Common cross-section solutions for columns

Some of the most important advantages of hollow sections are the following ones:

the geometrical characteristics of the cross-section and the stiffness about the

two main axes are comparable;

they have a much better behaviour to accidental torsion, compared to the open

ones;

an improved resistance against fire and against corrosion.

In many cases, hollow sections are filled with concrete, which leads to a better

rigidity and an increased fire resistance.

The main drawback of hollow sections is related to more complicate joint details

when connecting the column to the beams, to braces or to the foundation.

The cross-sections of columns should be class 1 or class 2. In zones where

plastic deformations are accepted (near the connection to the foundation and at the

top end) the cross-section should be class 1.

The connections of columns should be placed neither in strongly loaded

zones (neighbour to joints), nor in potentially plastic ones. Generally, this

recommendation is obeyed if the connection of the column is placed in a zone

between H/5 and H/3 above the floor (where H is the storey height), which

corresponds to a distance of 0,8 1,2m.

The column connections may be either welded or bolted; bolted connectionsuse high strength bolts in slip connections and the transfer of loads can be realised

either through the splices or by contact between parts.

Columns should be connected at each floor in the plane normal to the frame

plane.

The cross-section of the part of column where plastic deformations are

accepted should have a shape that allows reducing the amount of stresses caused

by the axial force and the shear force, compared to stresses caused by the bendingmoment. The length of the plastic zone should be limited at 1,5hc, where hcis the


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height of the column cross-section. Stiffeners should be placed all along the plastic

zone at a gap less than 0,5hcamong them.

1.5.2. Recommendations for column checks

1.5.2.1. General checks